Date of Award
2015
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Graduate Group
Physics & Astronomy
First Advisor
Mirjam Cvetic
Second Advisor
Justin Khoury
Abstract
In this dissertation, we systematically construct and study global F-theory compactifications with abelian and discrete gauge groups. These constructions are of fundamental relevance for both conceptual and phenomenological reasons.
In the case of abelian symmetries, we systematically engineer compactifications that support U(1)$\times$U(1) and U(1)$\times$U(1)$\times$U(1) gauge groups. The engineered geometries are elliptic fibrations with Mordell-Weil group rank two and three respectively. The bases of the fibrations are arbitrary, but as proofs of concept, we explicit create examples with bases $\mathbb{P}^2$ and $\mathbb{P}^3$. We study the low energy physics of these compactifications, we calculate the matter spectrum and confirm that it is anomaly free. In 4D compactifications, the $G_4$ flux is designed and the existence of Yukawa couplings is verified.
We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with
their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D
polyhedra. We present a base-independent analysis of the codimension one, two and three
singularities of these fibrations. We
explore the network of Higgsings relating these theories. Such Higgsings geometrically correspond
to extremal transitions induced by blow-ups in the 2D toric varieties. The discrete gauge groups $\mathbb{Z}_3$ and $\text{U(1)} \times \mathbb{Z}_2$ are naturally found when $\mathbb{P}^2$ and $\mathbb{P}^1\times\mathbb{P}^1$ are used as fiber ambient spaces. We also find the first realization of matter with U(1) charge three.
Finally, we study the discrete gauge group $\mathbb{Z}_3$ in detail. We find the three elements of the Tate-Shafarevich (TS) group. We make use of the Higgs mechanism with the charge three hypermultiplets and the Kaluza-Klein reduction from 6D to 5D. The results are interpreted from the F- M- theory duality perspective. In F-theory, compactifications over any of the three elements of the TS groups yield the same low energy physics, however, M-theory compactifications over the same elements give rise to different gauge groups.
Recommended Citation
Piragua, Hernan Augusto, "On Abelian and Discrete Symmetries in F-Theory" (2015). Publicly Accessible Penn Dissertations. 1949.
https://repository.upenn.edu/edissertations/1949